During certain medical procedures, such as radical cardio pulmonary surgery, it is conventional practice to remove venous blood from a patient, pass it through apparatus, and return same as arterial blood, the apparatus simulating the function of the human lungs to remove, principally, carbon dioxide from the blood and add oxygen thereto. Also, it may serve as a pump to provide a differential pressure between inlet venous blood and outlet arterial blood. Further, by choice of a suitable fluid supplied to the apparatus, it may serve for blood dialysis, simulating the function if kidneys, in instances of renal failure. Such apparatus has been fabricated in various forms among which include the apparatus disclosed in U.S. Pat. Nos. 3,771,658 and 3,771,899, both of which have issued to Robert C. Brumfield. Briefly, such apparatus comprises a cylindrical rotor having a semi-permeable membrane at its peripheral surface, which is mounted eccentrically in a surrounding cylindrical housing, means for supplying blood to the space therebetween for residence with the membrane, and means for supplying a secondary fluid, such as oxygen or a dialysis liquid, to the interior of the rotor. The second patent differs from the first principally in that the rotor is also mounted eccentrically on its drive shaft which effects a pulsating pumping pressure, rather than a constant pumping pressure. Other art is also disclosed in patent application Ser. No. 894,023 of Allen C. Billmeyer for Blood Processing Apparatus (filed concurrently herewith) which relates to an improvement on the patents referred to in that the rotor is formed with angularly spaced ribs, forming flutes therebetween, which materially increase the mass transfer area, as compared to a right circular cylinder of the same diameter and length having a membrane only at its outer cylindrical envelope surface.